Ace Calculus 3 In 16 Hours (The Complete Course)

Study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions

What you'll learn

Express a sequence as an order of numbers

Express an order of numbers as a sequence

Determine whether a sequence converges or diverges

Prove whether a sequence is monotonic or bounded

Find the convergence of a sequence

Express a series in sigma notation

Find the sum of a geometric or telescoping series

Test for the convergence of a series using the Test for Divergence, Integral Test, Comparison/Limit Comparison Tests, Alternating Test, Root and Ratio Tests

Estimate the Sum of a Series

Estimate the Sum of an Alternating Series

Find the radius of convergence and interval of convergence of a power series

Represent a function as a Taylor Series and Maclaurin Series

Estimate how close the function is to its Taylor series representation using the Taylor's Inequality

Apply the Taylor polynomials

Perform operations on vectors (dot product, projection, and cross product)

Recognize and understand equations of lines and planes in 3D

Recognize and sketch a surface function (a function of two variables)

Take the derivative and integral of a vector function

Find the arc length, curvature, and torsion of a vector function

Use and understand the Frenet-Serret equations

Sketch functions of two variables as surfaces and level curves

Take the partial derivative of a multivariable functions with respect to different variables

Use partial derivatives to find the equation of tangent planes

Apply the chain rule on multivariable functions

Find the gradient vector and directional derivatives

Maximize and minimize a multivariable function

Apply Lagrange multiplier method

Estimate the volume under a surface using double Riemann sum

Evaluate iterated integrals

Evaluate double integrals over general regions

Evaluate double integrals in polar coordinates

Find the surface are of a two-variable function over a region

Requirements

Calculus 1 (limits and derivatives)

Calculus 2 (integrals)

Familiarity with vector geometry or linear algebra

Description

HOW THIS COURSE WORK:This course, Ace Calculus 3 in 16 Hours (The Complete Course), is intended to introduce the student to the study of infinite sequences and series, vector functions, and derivatives and integrals for multivariable functions. The course includes videos, notes from whiteboard during lectures, and practice problem sets (with solutions!). I also show every single step in examples and proofs. The course is organized into the following topics:Section 2: Infinite SequencesConvergence of a sequenceProperties of a sequence: monotonic and boundedSection 3: Infinite SeriesSpecial series: geometric series, telescoping series, harmonic seriesSix convergence/divergence tests: test for divergence, integral test, comparison test, limit comparison test, alternating test, ratio test, and root testSection 4: Power SeriesTaylor series and Maclaurin seriesTaylor’s inequalityThree methods: direct computation, use term-by-term differentiation/integration, and use summation, multiplication, and division of power seriesSection 5: Vectors and the Geometry of SpaceVectorsOperations of vectors: the dot product, projection, and cross productEquations of lines and planes in 3DSurfaces in 3DSection 6: Vector FunctionsDerivative and integral of vector functionsThe arc length and curvatureFrenet-Serret EquationsMotion in Space: Velocity and AccelerationSection 7: Partial DerivativesMultivariable functionsPartial derivativesInterpretations of partial derivativesTangent planesLinear approximationsChain ruleDifferentiationThe gradient vector and directional derivativesFinding extreme values of a multivariable functionLagrange multipliersSection 8: Multiple IntegralsDouble Riemann sumEstimating the volume under a surfaceIterated/double integralsDouble integral over general regionsDouble integrals in polar coordinatesSurface areaCONTENT YOU WILL GET INSIDE EACH SECTION:Videos: I start each topic by introducing and explaining the concept. I share all my solving-problem techniques using examples. I show a variety of math issue you may encounter in class and make sure you can solve any problem by yourself.Notes: In each section, you will find my notes as downloadable resource that I wrote during lectures. So you can review the notes even when you don't have internet access (but I encourage you to take your own notes while taking the course!).Assignments: After you watch me doing some examples, now it's your turn to solve the problems! Be honest and do the practice problems before you check the solutions! If you pass, great! If not, you can review the videos and notes again before moving on to the next section.THINGS THAT ARE INCLUDED IN THE COURSE:An instructor who truly cares about your successLifetime access to Ace Calculus 3 in 16 Hours (The Complete Course)HIGHLIGHTS:#1: Downloadable lectures so you can watch the videos whenever and wherever you are.#2: Downloadable lecture notes so you can review the lectures without having a device to watch/listen.#3: Seven problem sets at the end of each section (with solutions!) for you to do more practice.#4: Step-by-step guide to help you solve problems.See you inside the course!- Gina :)

Overview

Section 1: Introduction

Lecture 1 Overview

Lecture 2 Welcome and How It Works

Lecture 3 Tips to Maximize Your Learning

Section 2: Infinite Sequences

Lecture 4 Downloadable Notes

Lecture 5 Overview of Section 2

Lecture 6 Sequences

Lecture 7 Convergence of a Sequence

Lecture 8 Examples: Convergence of a Sequence

Lecture 9 Monotonic and/or Bounded Sequence

Section 3: Infinite Series

Lecture 10 Downloadable Notes

Lecture 11 Overview of Section 3

Lecture 12 Series

Lecture 13 Geometric Series

Lecture 14 Telescoping Series

Lecture 15 Harmonic Series

Lecture 16 1. Test for Divergence

Lecture 17 2. Integral Test

Lecture 18 Estimating the Sum of a Series

Lecture 19 3. Comparison Test

Lecture 20 4. Limit Comparison Test

Lecture 21 5. Alternating Test

Lecture 22 Estimating the Sum of an Alternating Series

Lecture 23 Absolute Convergence

Lecture 24 6. Ratio Test

Lecture 25 7. Root Test

Lecture 26 Summary of Tests and Strategy for Testing Series

Section 4: Power Series

Lecture 27 Downloadable Notes

Lecture 28 Overview of Section 4

Lecture 29 Power Series

Lecture 30 Examples: Radius of Convergence and Interval of Convergence

Lecture 31 Representations of Functions as Power Series

Lecture 32 Taylor Series and Maclaurin Series

Lecture 33 Taylor's Inequality

Lecture 34 Method 1: Direct Computation

Lecture 35 Method 2: Use Term-by-term Differentiation and Integration

Lecture 36 Summary of Important Maclaurin Series

Lecture 37 Method 3: Use Summation, Multiplication, and Division of Power Series

Lecture 38 Applications of Taylor Polynomials

Section 5: Vectors and the Geometry of Space

Lecture 39 Downloadable Notes

Lecture 40 Overview of Section 5

Lecture 41 Three-Dimensional Coordinate Systems

Lecture 42 Examples: Surfaces in R3

Lecture 43 Vectors

Lecture 44 The Dot Product

Lecture 45 Projections

Lecture 46 The Cross Product

Lecture 47 Examples: The Cross Product

Lecture 48 Equation of Lines

Lecture 49 Equation of Planes

Lecture 50 Cylinders and Quadric Surfaces

Section 6: Vector Functions

Lecture 51 Downloadable Notes

Lecture 52 Overview of Section 6

Lecture 53 Vector Functions

Lecture 54 Derivatives of Vector Functions

Lecture 55 Integrals of Vector Functions

Lecture 56 Arc Length

Lecture 57 Arc Length Parametrization

Lecture 58 Curvature

Lecture 59 Another Formula for the Curvature

Lecture 60 Curvature for a Plane Curve

Lecture 61 The Normal and Binormal Vectors

Lecture 62 Frenet-Serret Equations

Lecture 63 Motion in Space: Velocity and Acceleration

Lecture 64 Tangential and Normal Components of Acceleration

Section 7: Partial Derivatives

Lecture 65 Downloadable Notes

Lecture 66 Overview of Section 7

Lecture 67 Multivariable Functions

Lecture 68 Visualizing Functions of Two Variables

Lecture 69 Limits of Two-Variable Functions

Lecture 70 Continuity of Two-Variable Functions

Lecture 71 Partial Derivatives

Lecture 72 Interpretations of Partial Derivatives

Lecture 73 Higher Derivatives

Lecture 74 Tangent Planes

Lecture 75 Linear Approximations

Lecture 76 Differentials

Lecture 77 The Chain Rule

Lecture 78 Examples: The Chain Rule

Lecture 79 Implicit Differentiation

Lecture 80 The Gradient Vector and Directional Derivatives

Lecture 81 Maximizing the Directional Derivative

Lecture 82 Tangent Planes to Level Surfaces

Lecture 83 Maximum and Minimum Values

Lecture 84 Examples: Maximum and Minimum Values

Lecture 85 Absolute Maximum and Minimum Values

Lecture 86 Lagrange Multipliers

Lecture 87 Examples: Lagrange Multipliers

Lecture 88 Lagrange Multipliers with Two Constraints

Section 8: Multiple Integrals

Lecture 89 Downloadable Notes

Lecture 90 Overview of Section 8

Lecture 91 Double Riemann Sum and Double Integrals over Rectangles

Lecture 92 Estimate Volume of the Solid Under a Surface

Lecture 93 Average Value

Lecture 94 Iterated Integrals

Lecture 95 Fubini’s Theorem

Lecture 96 A Special Case: Separation of Variables

Lecture 97 Double Integral over General Regions

Lecture 98 Examples: Double Integral over General Regions

Lecture 99 Properties of Double Integrals

Lecture 100 Double Integrals in Polar Coordinates

Lecture 101 Double Integrals in Polar Coordinates over General Regions

Lecture 102 Surface Area

Section 9: Conclusion

Lecture 103 Thank You & Good Luck & Next Step

Lecture 104 BONUS

Anyone who has completed calculus 1 (limits and derivatives) and calculus 2 (integrals) and wants to learn some more advanced math,Current Calculus 3 students who are looking for extra help,Anyone who is not in the science stream but wants to study calculus for fun